Winter 2019 USPAS Session

Integrable Particle Dynamics in Accelerators

January 28 - February 1, 2019 

(DRAFT PLAN)

Monday Jan  28, 2019

9:00 to 10:15 Part 1: Introduction

1.       Overview

2.       Courant-Snyder invariant

3.       Betatron tune

10:15 to 10:30 Break

10:30 to 12:00 Part 2: Integrals of motion

1.       Overview

2.       Hamiltonian dynamics

3.       Action-angle variables

12:00 to 13:30 Lunch

13:30 to 14:45 Part 3: Nonlinear oscillations and maps

15:00 to 15:15 Break

15:15 to 17:00 Part 4:

17:00 to 19:00 Dinner

Homework Problem Set 1

Tuesday Jan 29, 2019

9:00 to 9:30 Homework Review

9:30 to 10:15 Part 1: Integrable Autonomous Hamiltonian Systems

10:15 to 10:30 Break

10:30 to 12:00 Part 2: Integrability in Accelerators

12:00 to 13:00 Lunch

13:00 to 14:45 Computer Lab Session 1: Mappings

1.       Linear map

2.       Standard map

3.       Logistic map

4.       Mandelbrot

5.       2x mod 1 map

6.       Gingerbreadman map

14:45 to 15:00 Break

15:00 to 17:00 Part 3: Symplectic mappings of the plane

17:00 to 19:00 Dinner

Homework Problem Set 2

Wednesday Jan 30, 2019

9:00 to 9:30 Homework Review

9:30 to 10:15 Part 1: Integrable Maps in 2D

1.       McMillan equation

2.       McMillan map

3.       Danilov theorem

10:15 to 10:30 Break

10:30 to 12:00 Part 2: Integrable Maps in 4D

1.       Symplecticity in 4D

2.       Integrable but unstable systems

12:00 to 13:30 Lunch

13:30 to 14:45 Computer Lab Session 2:

1.       Poincare surface of section

2.       Integrable optics with quadrupoles, (.opt file)

3.       Integrable focusing with octupoles

4.       Henon-Heiles 1964 Paper

14:45 to 15:00 Break

15:00 to 17:00 Lecture

1.       IOTA concepts

2.       Integrable Ring Design

17:00 to 19:00 Dinner

Homework Problem Set 3

Thursday Jan 31, 2019

9:00 to 9:30 Homework Review

9:30 to 10:15 Part 1:  

10:15 to 10:30 Break

10:30 to 12:00 Part 2: Integrable and Chaotic mappings (large file!)

12:00 to 13:30 Lunch

13:00 to 14:45 Part 3: Practical applications to accelerators

14:45 to 15:00 Break

15:00 to 17:00

17:00 to 19:00 Dinner

Homework Problem Set 4

Friday FEB 1, 2019

9:00 to 12:00 Final Exam

References

1.       B. Chirikov, A UNIVERSAL INSTABILITY OF MANY-DIMENSIONAL OSCILLATOR SYSTEMS, Phys. Reports 52, 263-379 (1979). (PDF, 10MB)

2.       R. Ruth, SINGLE PARTICLE DYNAMICS IN CIRCULAR ACCELERATORS, SLAC-PUB-4103, 1986 (PDF, 3.5MB)

3.       E. McMillan, A Problem in the Stability of Periodic Systems, 1971 (PDF, 1.2MB)

4.       R. Beth, Complex Potentials, (PDF, 6MB)

 

 

 

 

 



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